Weyl space forms and their submanifolds

Isotropic Lagrangian Submanifolds in Complex Space Forms

In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.

Umbilicity of (Space-Like) Submanifolds of Pseudo-Riemannian Space Forms

We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...

An inequality between Willmore functional and Weyl functional for submanifolds in space forms

Let φ : M → Rn+p(c) be an n-dimensional submanifold in an (n + p)dimensional space form Rn+p(c) with the induced metric g. Willmore functional of φ is W (φ) = ∫M (S − nH2)n/2dv, where S = ∑ α,i, j (h α i j ) 2 is the square of the length of the second fundamental form, H is the mean curvature of M . The Weyl functional of (M, g) is ν(g) = ∫M |Wg|n/2dv, where |Wg|2 = ∑ i, j,k,l W 2 i jkl and Wi ...

Shape Operator of Slant Submanifolds in Kenmotsu Space Forms

Contact CR-Warped product submanifolds in Kenmotsu space forms

Abstract: In the present paper, we give a necessary and sufficient condition for contact CR-warped product to be contact CR-product in Kenmotsu space forms.